Your TP/SL Ratio Is Not a Strategy

There is a certain kind of trading video that sounds reasonable right up until you do the math. The pitch is familiar: make your take profit bigger than your stop loss, keep the “reward-to-risk” ratio above 2:1 or 3:1, and the profits will take care of themselves. “I only need to be right one trade out of three.” Sometimes there is a whiteboard. Sometimes there is a rented car in the thumbnail.

The arithmetic is not wrong. A 3:1 payoff really does break even at a 25% win rate before costs. The problem is that the market does not owe you that win rate. If price is a fair random walk, making the take profit farther away makes the winning exit rarer by exactly the amount required to cancel the bigger payoff.

That is the part the ratio pitch leaves out. A bracket order is a risk-control tool. It is not a signal.

This post walks through the math, then gives you a small browser simulator. Set the brackets. Add round-trip cost. Run a few simulated traders. The lesson is not that take profits and stop losses are useless. The lesson is that the ratio alone has no edge.

The claim we are testing

The strategy usually looks like this. Pick an entry. Once the position is open, attach an OCO bracket: a take profit on one side and a stop loss on the other. Make the take profit wider than the stop. Now the trade has a nice-looking reward-to-risk ratio.

For example, suppose you risk $100 to make $300. The sales pitch says you can be wrong most of the time and still come out ahead.

That statement is incomplete. It is true only if your actual probability of hitting the $300 target is greater than 25% after costs. On a fair price process, it is exactly 25% before costs. Add commissions, fees, spread, slippage, or stop-market overfill, and the required win rate moves above 25%.

So the real question is not “is my TP bigger than my SL?” The real question is “does my entry condition make the TP more likely to hit than fair geometry says it should?”

The six-line version of the math

Let the take profit be a dollars above entry and the stop loss be b dollars below entry. Start the price at zero. Assume a fair price process: no drift, no prediction, exact fills, and no gaps through the bracket.

Let p be the probability that price hits +a before -b. At the first exit, the stopped price is either +a or -b. A fair process remains fair when stopped at those bounded barriers, so:

E[stopped price] = p · a + (1 - p) · (-b) = 0

Solving for p:

p = b / (a + b)

That is the whole trick. The farther the target is, the less often it hits. The closer the stop is, the more often it hits.

Now compute expected value before costs:

EV = p · a - (1 - p) · b
   = [b / (a + b)] · a - [a / (a + b)] · b
   = 0

The payoff ratio changes the shape of the distribution. It does not change the expectancy.

Here are the same numbers in table form:

Add a fixed round-trip cost c, and the formula becomes:

EV = p · a - (1 - p) · b - c

The break-even win rate is therefore:

p_break_even = (b + c) / (a + b)

That is the practical version. With a $300 target, $100 stop, and $10 of all-in trading friction, the fair win rate is 25.0%, but the break-even win rate is 27.5%. The missing 2.5 percentage points have to come from a real edge. The ratio does not create them.

Run it yourself

The simulator below samples the exact first-hit distribution implied by the math above. It is not simulating every tick of a random walk; doing that for thousands of trades would be slow and would estimate the same barrier probability less cleanly. Instead, each completed trade is sampled with the fair win probability b / (a + b), then the cost is subtracted.

A few things are worth watching.

First, the empirical win rate moves toward the fair win rate. A 3:1 bracket does not keep a 50% win rate. A 1:3 bracket does not magically become high-quality just because most trades are green. The win frequency is part of the same equation as the payoff size.

Second, the individual paths spread out. With zero cost, some traders finish up and some finish down even though all of them are running the same zero-edge process. That is survivorship bias in miniature. The lucky paths get screenshots. The unlucky paths disappear.

Third, the mean final P&L is noisy when you only simulate a small number of paths. Increasing the number of trades per path makes each trader’s average P&L per trade converge, but the dollar dispersion of final P&L grows roughly like sqrt(N). To make the displayed mean itself stabilize, increase the number of simulated paths, not just the number of trades.

Finally, turn on costs. If round-trip friction is $10, then the expected drag is $10 per completed trade. Over 2,000 trades, that is $20,000 of expected loss. The cloud does not merely wander; it leans downward.

Kelly will not rescue a zero-edge bracket

The usual next defense is bet sizing. “Fine, the raw strategy has no edge, but I can size intelligently.”

Kelly sizing does not create edge. It sizes edge that already exists.

For a binary payoff where the win is b times the loss, the Kelly fraction is:

f* = (b · p - q) / b

Here b = TP / SL, p = SL / (TP + SL), and q = TP / (TP + SL). Therefore:

b · p = q

So f* = 0. The Kelly answer is: do not bet.

With costs, the bracket has negative expectancy. In a textbook betting problem, a negative Kelly fraction sometimes means “take the other side.” In trading, the inverse bracket usually pays the same friction, crosses the same spread, and suffers the same execution risks. Flipping direction does not make the toll booth disappear.

This is also why martingale sizing, doubling after losses, scaling after wins, and “optimal f” (or optimal fixed fraction) variants do not change the conclusion. They alter the path of returns. They do not change the expected value of a fair game after costs.

There is a related geometric point: even a zero-arithmetic-EV bet has negative expected log growth for any nonzero sizing fraction. That is Jensen’s inequality showing up in your brokerage account. Kelly returns zero because the growth-optimal allocation to a fair risky bet is no allocation.

Risk of ruin: zero EV is not safe

A zero-EV strategy can still be dangerous with finite capital. Over an infinite horizon, a fair one-dimensional random walk with fixed bet size will hit any finite drawdown level almost surely. With trading costs, the process has negative drift, so the same drawdown arrives faster.

For a real futures account, “ruin” is usually not literal bankruptcy. It is a margin call, a trailing drawdown breach, a prop-firm daily loss limit, or the point where the trader stops following the system. Those are absorbing barriers too.

Be careful with simple ruin formulas here. The textbook formula (q / p)^B is often quoted in the wrong direction, and it applies to a particular equal-step gambler’s-ruin model. Bracket trades with unequal wins and losses, commissions, slippage, margin constraints, and trailing drawdowns are not that model. The qualitative conclusion is enough: without edge, repeated exposure plus finite capital eventually finds the boundary.

What would make the bracket matter?

You need something that breaks the fair-random-walk assumption. The bracket can then be useful, but the edge is coming from the condition that changes the probabilities or the fills, not from the ratio by itself.

Directional prediction. Your entry signal might make the upper barrier more likely than fair geometry predicts. For a $300 target and $100 stop, fair is 25%. If your tested, out-of-sample, after-cost win rate is 31%, the bracket has positive expectancy. If it is 25%, it does not.

Time horizons and volatility. In the no-time-limit model, volatility changes how fast a bracket gets hit, not the expected value of which side hits first. Volatility starts to matter when you add a session close, a time stop, opportunity cost, volatility-dependent slippage, or an entry rule that only triggers in certain regimes. A breakout system can be a volatility strategy, but only because the entry and holding rule create exposure to realized movement. The bracket ratio alone still does not.

Execution quality. Stops are not magic barriers. In fast markets, stop orders can fill through the stop level. Targets may be limit orders sitting in a queue. Slippage can be asymmetric: losses realize worse than modeled, while wins do not receive equivalent price improvement. That pushes expectancy down unless your model explicitly accounts for it.

Jumps, tails, and serial dependence. Heavy tails by themselves do not repeal optional stopping. If the price process is still a martingale and fills are exact, the fair-game argument survives. What can matter is non-martingale structure: trend persistence, mean reversion, jump asymmetry, volatility clustering, or conditional drift after your entry event. That is where trend-following and mean-reversion systems live. The distribution is doing the work, not the ratio.

Selection effects. If a thousand traders run the same zero-edge bracket system, some will look brilliant for a while. The winners are visible because they have something to post. The losers are quiet. A profitable-looking path is not the same thing as a positive-expectancy process.

The gurus get one thing right

The ratio does change the experience of trading.

A 1:5 TP/SL bracket wins often and occasionally takes a large loss. It feels consistent until the loss arrives. A 5:1 bracket loses often and occasionally pays out. It feels terrible even when it is behaving exactly as designed.

That difference matters psychologically. High-win-rate systems are easier to sell because they generate lots of green screenshots. Low-win-rate systems are harder to sit through because the trader spends most of the time being wrong. But neither experience is an edge.

The bracket chooses the emotional texture of the P&L path. The signal chooses whether the path has positive expectancy.

Bottom line

If someone tells you a strategy is profitable because the take profit is larger than the stop loss, they have not shown you an edge. They have shown you a payoff shape.

The fair win rate moves against the payoff ratio. Costs move the break-even win rate even farther away. Position sizing cannot fix it. A lucky equity curve cannot prove it.

A bracket is useful once you have a real signal. It defines how you express the edge, how much variance you tolerate, and what kind of mistakes you are willing to make. But it is not the source of the edge.

When you have a strategy that actually has positive expectancy and want to automate it from TradingView into NinjaTrader 8, CrossTrade is the infrastructure that delivers your signals in 34 milliseconds on average. New to CrossTrade? Start your free 7-day trial.

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